Interpreting the summary() of a lm() linear model in R

Question

I have a multiple linear regression with 4 independent variables. The summary() function returns the following:

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.03039    0.16152  -0.188   0.8530    
var1         -0.96553    0.18595  -5.193 7.34e-05 ***
var2        -0.25014    0.19732  -1.268   0.2220  *  
var3         -0.40355    0.22072  -1.828   0.0851 **  
var4         0.15887    0.18559   0.856   0.4039    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5606 on 17 degrees of freedom
Multiple R-squared:  0.7572,    Adjusted R-squared:  0.6857 
F-statistic:  10.6 on 5 and 17 DF,  p-value: 9.445e-05

It shows that var4 is not significant. However, when I remove it from the model, the new p-value increases, R-square decreases, and the mean squared error of the model also increases

Question: Should I keep or remove var4 from the model? Will my model be criticized if I keep a non-significant independent variable? Thanks